Excursions in Number Theory

by C. Stanley Ogilvy, John T. Anderson

"A splendidly written, well selected and presented collection … I recommend the book unreservedly to all readers, in or out of professional mathematics, who like to 'follow the gleam' of numbers." — Martin Gardner.
The theory of numbers is an ancient and fascinating branch of mathematics that plays an important role in modern computer theory. It is also a popular topic among amateur mathematicians (who have made many contributions to the field) because of its it does not require advanced knowledge of higher mathematics.
This delightful volume, by two well-known mathematicians, invited readers to join a challenging expedition into the mystery and magic of number theory. No special training is needed — just high school mathematics, a fondness for figures, and an inquisitive mind. Such a person will soon be absorbed and intrigued by the ideas and problems presented here.
Beginning with familiar notions, the authors skillfully yet painlessly transport the reader to higher realms of mathematics, developing the necessary concepts along the way, so that complex subjects can be more easily understood. Included are thorough discussions of prime numbers, number patterns, irrationals and iterations, and calculating prodigies, among other topics.
Much of the material presented is not to be found in other popular treatments of number theory. Moreover, there are many important proofs (presented with simple and elegant explanations) often lacking in similar volumes. In sum, Excursions in Number Theory offers a splendid compromise between highly technical treatments inaccessible to lay readers and popular books with too little substance. Its stimulating and challenging presentation of significant aspects of number theory may be read lightly for enjoyment or studied closely for an exhilarating mental challenge.

Genres: Mathematics, Science, Nonfiction, Number Theory

192 pages, Paperback

First published January 1, 1966

Reviews

[David Mario Mendiola · Rating 4 out of 5]

A fun journey. I felt like a boy scout out camping, learning about all the trees and bugs close to the campsite. Then at night by the campfire, the experienced troop master (is that what he's called? I flunked out of cub scouts) tells thrilling stories of number problems that haven't been solved, still lurking out there in the untamed forest, and will sneak into your tent and eat you.

[Jherane Patmore · Rating 4 out of 5]

Loads of fun! I started this last year and picked it back up again today. It has very simple concepts that breakdown a lot of the "why" we think of numbers the way we do. I think this will be one of the books I re-read and enjoy in years to come.

[Alex · Rating 4 out of 5]

This book is a fun romp through number theory. Don't be fooled by the short chapters, the book packs a few punches. But it's still an accessible intro to the field. While the data related to finding primes by computer is hopelessly out of date, the rest of the material is still very relevant. It was a lucky find in a second hand book store, and together with Lara Alcock's book, it rekindled my interest in maths.

[Suzza · Rating 5 out of 5]

This was one of the first books on mathematics that I purchased. The title sounds like it is going to be difficult. It is very simple and straightforward. You don't need to know more about math than what you learned in school.

I highly recommend this book to anyone who is curious about mathematics.

[Kevin Fitzsimmons · Rating 5 out of 5]

Not a cover to cover read, but a lot of fun to play around with. Enjoyable.

[Rakibul Dolon · Rating 1 out of 5]

অনেক বাজে অনুবাদ। ছোটভাইকে দেব বলে কিনেছিলাম। কিন্তু ভাষার যা প্রয়োগ!
কেজি দরে বেঁচে দেয়া লাগবে এখন।

[Brian Barnett · Rating 3 out of 5]

Didn't learn much I didn't already know, but this was a nice refresher that reinvigorated my interest in number theory. I especially love how the book ends: "What if a study is not of earth-shaking importance? If it stimulates the imagination and whets the appetite for more, is not that enough? Do we dare to hope that this book has done as much for you? Have we cast a little light on what was formerly dim, so that you now wish you knew more about some of these things? The path is endless, but many rewards are offered along the way. One could do worse than follow the gleam of numbers."

[Dean Allison · Rating 2 out of 5]

Read this one sitting on my porch, flaking the pages between my fingers while sipping lemonade. I filled a legal pad with ideas, mainly repetitive ones from this book. The premise is a body of knowledge: science. This is why the title contains "excursion." Used it as a bookend to pastimes.

[Andrea Valente · Rating 4 out of 5]

Terrific book. Made me refresh a lot of my number theory... inductive proves are just fun to read and play with.
I particularly liked the parts about continuous fractions (which I should really learn better!) and modular algebra.

A very accessible and clear book.

[Liammooney · Rating 5 out of 5]

A hilarious and delightful romp through a magical land of gumdrops and integers.

[Matt Young · Rating 5 out of 5]

I loved this book. A very simple and very fun read on elementary Number Theory. Good discussion on primes and Fibonacci. Recommend!